Regions:
I noticed a few crabs had egg sizes that were much higher than others, so going to recalculate the volume from the egg dimensions to compare.
So the excel file on the dropbox has some inconsistencies with the estimated fecundity, and other columns that were drag-down in excel.
The values that appeared much higher have the correct volume calculations, the others have something different.
finish analysis with new_vol.
Pull Crab Specific Fecundity Details:
For analyses relating to egg characteristics (egg volume, estimated fecundity), measurements will be the mean value for each crab to avoid dealing with repeated measures.
Estimated fecundity ranged from 1.075 - 8.929 million eggs.
With mean fecundity of 3.268 +/- 0.148 millions of eggs.
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | -4903271.27 | 1014566.887 | -4.832871 | 7.5e-06 |
| Carapace_width | 51881.44 | 6405.776 | 8.099166 | 0.0e+00 |
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 12.0828802 | 0.3259837 | 37.065901 | 0 |
| Carapace_width | 0.0181998 | 0.0019443 | 9.360718 | 0 |
Delta AIC for log-link - gaussian models = 9.65
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 11.8221003 | 0.3503094 | 33.7475992 | 0.0000000 |
| Carapace_width | 0.0194279 | 0.0018893 | 10.2832958 | 0.0000000 |
| regionLouisiana | 0.0363446 | 0.1550486 | 0.2344080 | 0.8153726 |
| regionMS Bight | -0.1780774 | 0.1817878 | -0.9795894 | 0.3307612 |
| regionTexas | 0.1358823 | 0.1543131 | 0.8805625 | 0.3816563 |
If we include region in the model we get kind of a weird result, that being that carapace width is no longer significant:
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 13.5008959 | 1.2522673 | 10.7811611 | 0.0000000 |
| Carapace_width | 0.0093685 | 0.0076467 | 1.2251764 | 0.2249299 |
| regionLouisiana | -1.6809199 | 1.3620065 | -1.2341496 | 0.2215907 |
| regionMS Bight | 0.2181973 | 1.6094676 | 0.1355711 | 0.8925793 |
| regionTexas | -1.8680225 | 1.3186960 | -1.4165680 | 0.1613842 |
| Carapace_width:regionLouisiana | 0.0102844 | 0.0082595 | 1.2451667 | 0.2175408 |
| Carapace_width:regionMS Bight | -0.0023466 | 0.0098237 | -0.2388744 | 0.8119545 |
| Carapace_width:regionTexas | 0.0120422 | 0.0080441 | 1.4970240 | 0.1392274 |
Which is confusing because its pretty clear on its own.
Check Season as well just to be sure.
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 11.9795124 | 0.3528126 | 33.9543210 | 0.000000 |
| Carapace_width | 0.0182437 | 0.0019520 | 9.3459375 | 0.000000 |
| SeasonSummer | 0.1033463 | 0.1238141 | 0.8346898 | 0.406732 |
| Resid. Df | Resid. Dev | dAIC | weight |
|---|---|---|---|
| 68 | 4.573742e+13 | 0.0 | 0.56 |
| 65 | 4.263123e+13 | 0.9 | 0.36 |
| 71 | 5.238409e+13 | 3.9 | 0.08 |
| 71 | 5.978975e+13 | 13.6 | 0.00 |
(if we have fall egg sizes), we do not have enough (n = 5)
We also have repeated measures for measurements on each egg mass, so gonna have the eggmass/crabID as a random effect as they are likely correlated. Otherwise we could use the average egg measurements for each crab.
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 0.0089874 | 0.0004836 | 18.583181 | 0.00000 |
| Carapace_width | -0.0000101 | 0.0000031 | -3.314658 | 0.00094 |
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 0.0090056 | 0.0019002 | 4.7392833 | 0.0000107 |
| Carapace_width | -0.0000103 | 0.0000120 | -0.8545614 | 0.3956683 |
| effect | group | term | estimate | std.error | statistic |
|---|---|---|---|---|---|
| fixed | NA | (Intercept) | 0.0090054 | 0.0019002 | 4.7390351 |
| fixed | NA | Carapace_width | -0.0000103 | 0.0000120 | -0.8543744 |
| ran_pars | Unique_ID | sd__(Intercept) | 0.0017042 | NA | NA |
| ran_pars | Residual | sd__Observation | 0.0010002 | NA | NA |
Analysis of Variance Table
Df Sum Sq Mean Sq F value
Carapace_width 1 7.3021e-07 7.3021e-07 0.73
Data: eggdat
Models:
m1: new_vol ~ Carapace_width
m2: new_vol ~ Carapace_width + (1 | Unique_ID)
Df AIC BIC logLik deviance Chisq Chi Df Pr(>Chisq)
m1 3 -14101 -14086 7053.7 -14107
m2 4 -15767 -15746 7887.4 -15775 1667.5 1 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
This is the variance explained after the fixed effects : 74.39
Plot the overall relationship first
Region seems to have a viable impact, but it may just look that way because of an interaction effect with egg size.
I don’t think we will be able to tease this out with so many combinations with no data unless we re-bin into more general groups or drop regions like florida.
When you look at the interactions you get this mess:
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 0.0084412 | 0.0021032 | 4.0134820 | 0.0002045 |
| Carapace_width | -0.0000009 | 0.0000091 | -0.0943493 | 0.9252164 |
| Egg_stage2 | -0.0000809 | 0.0010699 | -0.0756063 | 0.9400402 |
| Egg_stage3 | -0.0022787 | 0.0018627 | -1.2233692 | 0.2270410 |
| Egg_stage4 | -0.0003083 | 0.0018868 | -0.1634093 | 0.8708683 |
| Egg_stage5 | -0.0000976 | 0.0014954 | -0.0652598 | 0.9482327 |
| Egg_stage6 | 0.0017296 | 0.0014954 | 1.1566106 | 0.2530393 |
| Egg_stage7 | 0.0008058 | 0.0011896 | 0.6773941 | 0.5013419 |
| Egg_stage8 | 0.0032515 | 0.0011402 | 2.8518326 | 0.0063469 |
| Egg_stage9 | 0.0050981 | 0.0011481 | 4.4402655 | 0.0000511 |
| regionLouisiana | -0.0025628 | 0.0018863 | -1.3586391 | 0.1804829 |
| regionMS Bight | -0.0068913 | 0.0014708 | -4.6854313 | 0.0000225 |
| regionTexas | -0.0019992 | 0.0011914 | -1.6779971 | 0.0997157 |
| Egg_stage2:regionLouisiana | 0.0006934 | 0.0015496 | 0.4474613 | 0.6565139 |
| Egg_stage3:regionLouisiana | 0.0037754 | 0.0022219 | 1.6991860 | 0.0956254 |
| Egg_stage6:regionLouisiana | 0.0002421 | 0.0020707 | 0.1169131 | 0.9074068 |
| Egg_stage7:regionLouisiana | 0.0015330 | 0.0017750 | 0.8636681 | 0.3919783 |
| Egg_stage8:regionLouisiana | 0.0003231 | 0.0016757 | 0.1928203 | 0.8478967 |
| Egg_stage9:regionLouisiana | -0.0016360 | 0.0017539 | -0.9327504 | 0.3555224 |
| Egg_stage2:regionMS Bight | 0.0054356 | 0.0014105 | 3.8537158 | 0.0003387 |
| Egg_stage3:regionMS Bight | 0.0072943 | 0.0019297 | 3.7800064 | 0.0004262 |
| Egg_stage4:regionMS Bight | 0.0051813 | 0.0021123 | 2.4528845 | 0.0177779 |
| Egg_stage5:regionMS Bight | 0.0053603 | 0.0015804 | 3.3917707 | 0.0013813 |
| Egg_stage3:regionTexas | 0.0033493 | 0.0016112 | 2.0786925 | 0.0429032 |
Call:
lm(formula = egg_volume ~ es_bins, data = fecunddat)
Residuals:
Min 1Q Median 3Q Max
-0.0023169 -0.0011691 -0.0005623 0.0010144 0.0053023
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0069257 0.0004597 15.066 <2e-16 ***
es_binsmiddle 0.0002403 0.0007623 0.315 0.754
es_binslate 0.0006282 0.0005190 1.211 0.230
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.00172 on 70 degrees of freedom
Multiple R-squared: 0.0226, Adjusted R-squared: -0.005321
F-statistic: 0.8095 on 2 and 70 DF, p-value: 0.4492
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 0.0070689 | 0.0038450 | 1.8384811 | 0.0704243 |
| Carapace_width | -0.0000009 | 0.0000247 | -0.0375176 | 0.9701839 |
| es_binsmiddle | -0.0009484 | 0.0056032 | -0.1692645 | 0.8660986 |
| es_binslate | 0.0043574 | 0.0046599 | 0.9351006 | 0.3530946 |
| Carapace_width:es_binsmiddle | 0.0000076 | 0.0000358 | 0.2134966 | 0.8315880 |
| Carapace_width:es_binslate | -0.0000235 | 0.0000297 | -0.7903333 | 0.4321217 |
This one is nice and cut-and-dry, just an ANOVA to test the group differences.
Call:
lm(formula = Percent_fert ~ molt_stage, data = fecunddat)
Residuals:
Min 1Q Median 3Q Max
-0.308537 -0.044737 0.005263 0.091463 0.100000
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.94474 0.02251 41.967 <2e-16 ***
molt_stage3 -0.03620 0.02723 -1.329 0.188
molt_stage4 -0.04474 0.03532 -1.267 0.209
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.09812 on 70 degrees of freedom
Multiple R-squared: 0.03062, Adjusted R-squared: 0.002922
F-statistic: 1.105 on 2 and 70 DF, p-value: 0.3368
Groups are unbalanced, and it throws a warning, but we’re probably ok.
| molt_stage | n |
|---|---|
| 2 | 19 |
| 3 | 41 |
| 4 | 13 |
Call:
lm(formula = Percent_fert ~ es_bins, data = fecunddat)
Residuals:
Min 1Q Median 3Q Max
-0.31274 -0.01429 0.03571 0.08725 0.14375
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.96429 0.02543 37.925 <2e-16 ***
es_binsmiddle -0.10804 0.04216 -2.562 0.0126 *
es_binslate -0.05154 0.02870 -1.796 0.0769 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.09513 on 70 degrees of freedom
Multiple R-squared: 0.08878, Adjusted R-squared: 0.06275
F-statistic: 3.41 on 2 and 70 DF, p-value: 0.03862
Call:
lm(formula = Percent_fert ~ region, data = fecunddat)
Residuals:
Min 1Q Median 3Q Max
-0.33429 -0.03429 0.04630 0.06571 0.09630
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.900000 0.056987 15.793 <2e-16 ***
regionLouisiana 0.003704 0.060070 0.062 0.951
regionMS Bight -0.012500 0.066823 -0.187 0.852
regionTexas 0.034286 0.059379 0.577 0.566
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.0987 on 69 degrees of freedom
Multiple R-squared: 0.03313, Adjusted R-squared: -0.008904
F-statistic: 0.7882 on 3 and 69 DF, p-value: 0.5046
This is a two-way crossed ANOVA comparing percent fertilization between egg stage bins and region with interactions.
# A tibble: 12 x 4
# Groups: region [?]
region es_bins n mean_fert
<fct> <fct> <int> <dbl>
1 Florida early 1 0.95
2 Florida middle 1 0.95
3 Florida late 1 0.8
4 Louisiana early 4 0.975
5 Louisiana middle 2 0.675
6 Louisiana late 21 0.912
7 MS Bight early 2 0.925
8 MS Bight middle 3 0.9
9 MS Bight late 3 0.85
10 Texas early 7 0.971
11 Texas middle 2 0.925
12 Texas late 26 0.925
Call:
lm(formula = Percent_fert ~ region * es_bins, data = fecunddat)
Residuals:
Min 1Q Median 3Q Max
-0.325 -0.025 0.025 0.075 0.100
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.500e-01 9.155e-02 10.376 4.26e-15 ***
regionLouisiana 2.500e-02 1.024e-01 0.244 0.8079
regionMS Bight -2.500e-02 1.121e-01 -0.223 0.8243
regionTexas 2.143e-02 9.788e-02 0.219 0.8274
es_binsmiddle 8.197e-16 1.295e-01 0.000 1.0000
es_binslate -1.500e-01 1.295e-01 -1.159 0.2512
regionLouisiana:es_binsmiddle -3.000e-01 1.518e-01 -1.976 0.0527 .
regionMS Bight:es_binsmiddle -2.500e-02 1.541e-01 -0.162 0.8717
regionTexas:es_binsmiddle -4.643e-02 1.488e-01 -0.312 0.7561
regionLouisiana:es_binslate 8.690e-02 1.388e-01 0.626 0.5335
regionMS Bight:es_binslate 7.500e-02 1.541e-01 0.487 0.6282
regionTexas:es_binslate 1.036e-01 1.352e-01 0.766 0.4467
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.09155 on 61 degrees of freedom
Multiple R-squared: 0.2646, Adjusted R-squared: 0.132
F-statistic: 1.995 on 11 and 61 DF, p-value: 0.04436